You have a strong need to separate out civil wars from great power conflicts, but many of them, particularly the ones that lead to lots of deaths, have very strong international involvement, and the destruction is driven in large part by foreign involvement. The Congo Wars and the Russian Civil War are good examples of this. Beyond that, you basically jump at the opportunity to classify wars as civil wars: the Germanic incursions into the Roman Empire and the Thirty Years' War [1] are in no way civil wars.

Placing importance of wars on the raw numbers of people killed is a bad way to go about things. First off, we have trouble establishing these counts even in modern contexts where sophisticated bureaucracies exist to keep track of everything (these bureaucracies have a way of breaking down in war); historical counts involve a fair amount of guesswork, and especially in list mode, you're not seeing similar methodologies being applied to ensure that the estimates are comparable. Even keeping track of wars with similar methodologies is difficult: why do we roll up all of the 14th century Anglo-French conflicts into the Hundred Years' War, yet insist on keeping World War I, World War II, the Russian Civil War, Second Sino-Japanese War, and the Spanish Civil War all separate instead of a Forty Years' War?

Most importantly, however, is that raw death totals don't reflect the impact of destruction. The deadliest war in US history is not the American Civil War, but King Philip's War, which killed 10% of the population. The Thirty Years' War was hardest in Northern Germany, where it killed about 50% of the people, while World War II only managed to kill 17% of the Poles (and most of that due to the Holocaust). Raw death counts inflate the relative importance of Chinese wars, since the Chinese river plains were historically able to support far larger population densities than in, say, Europe, so conflicts in China necessarily involve more people even at a comparable level of technological sophistication.

[1] For most of its existence, the Holy Roman Empire was not properly a country as we would understand it in our modern terminology. Admittedly, the Habsburgs were trying to reestablish it as a strong centralized state at the time, but the Thirty Years' War was effectively the point at which they gave up. It's more proper to think of the HRE at this point as closer to a 17th century organization akin to the current European Union than the modern United States.